Montgomery modular multiplication is one of the fundamental operations used in cryptographic processes, such as Rivest, Shamir and Adleman (RSA) and Elliptic Curve Cryptosystems. Since the introduction of the RSA process in 1978, high-speed and space-efficient hardware architectures for modular multiplication have been a subject of constant interest for almost 30 years. During this period, one of the most useful advances came with the introduction of the Montgomery multiplication process due to Peter L. Montgomery. Montgomery multiplication is a basic operation of modular exponentiation, which may be used in the RSA public-key cryptosystem. It may also be used in Elliptic Curve Cryptosystems, and several methods of factoring, such as Elliptic Curve Method (ECM), p−1, and Pollard's “rho” method, as well as in many other cryptographic and cryptanalytic transformations.